U.S. patent number 8,126,072 [Application Number 12/491,056] was granted by the patent office on 2012-02-28 for noise variance estimation in wireless communications for diversity combining and log likelihood scaling.
This patent grant is currently assigned to Qualcomm Incorporated. Invention is credited to Peter J. Black, Srikant Jayaraman, June Namgoong, Hao Xu.
United States Patent |
8,126,072 |
Namgoong , et al. |
February 28, 2012 |
Noise variance estimation in wireless communications for diversity
combining and log likelihood scaling
Abstract
The present patent application comprises a method and means for
demodulating symbols, comprising converting an OFDM symbol from a
time domain to a frequency domain, selecting pilot tones, making a
soft decision based on received data, and estimating a channel
frequency response. In another example, the method and means
further comprises selecting guard tones. In another example, the
method and means further comprises generating channel estimates for
in-band and band-edge pilot tones.
Inventors: |
Namgoong; June (San Diego,
CA), Xu; Hao (San Diego, CA), Black; Peter J. (San
Diego, CA), Jayaraman; Srikant (San Diego, CA) |
Assignee: |
Qualcomm Incorporated (San
Diego, CA)
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Family
ID: |
35519776 |
Appl.
No.: |
12/491,056 |
Filed: |
June 24, 2009 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20100054371 A1 |
Mar 4, 2010 |
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Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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11047347 |
Jan 28, 2005 |
7672383 |
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Current U.S.
Class: |
375/260 |
Current CPC
Class: |
H04B
1/1027 (20130101); H04L 1/20 (20130101); H04L
27/2647 (20130101) |
Current International
Class: |
H04L
27/28 (20060101) |
Field of
Search: |
;375/260,285,326,346,348,340 ;455/83,631,67.13,218 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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1420531 |
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May 2004 |
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EP |
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2000013353 |
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Jan 2000 |
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JP |
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2002026860 |
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Jan 2002 |
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JP |
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WO9956424 |
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Nov 1999 |
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WO |
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WO2004015946 |
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Feb 2004 |
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WO |
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Other References
International Search Report and Written Opinion--PCT/US05/033133,
International Search Authority--European Patent Office--Jan. 23,
2006. cited by other .
Weste, et al., "VLSI for OFDM," IEEE Communications Magazine, Oct.
1998, pp. 127-131. cited by other .
Zhen, A Novel Channel Estimation and Tracking Method for Wireless
OFDM Systems Based on Pilots and Kalman Filtering, 2003, IEEE, p.
17-20. cited by other .
Zou, et al., "COFDM: An Overview," Broadcasting, IEEE Transactions
on Broadcasting, vol. 41, No. 1, Mar. 1995, pp. 1-8. cited by other
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H. Rohling, et al., "Broad-Band OFDM Radio Transmission for
Multimedia Applications", Proceedings of the IEEE, vol. 87, No. 10,
Oct. 1999, pp. 1778-1789. cited by other .
S. Kaiser, et al., "Performance of multi-carrier CDMA systems with
channel estimation in two dimensions", Proc 8th IEEE International
Symposium on Personal Indoor and Mobile Radio Communications
(PIMRC), Helsinki, Finland, Sep. 1997, pp. 115-119. cited by other
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Stuber et al., "Broadband MIMO-OFDM Wireless Communications", IEEE
Proceedings, Section II B, IV A, V, VIA, Feb. 2004. cited by
other.
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Primary Examiner: Ahn; Sam K
Attorney, Agent or Firm: Beladi; Sayed H.
Parent Case Text
CLAIM OF PRIORITY UNDER 35 U.S.C. .sctn.119
The present application for patent is a continuation of, and claims
the benefit of priority from, U.S. patent application Ser. No.
11/047,347 entitled "Noise Variance Estimation in Wireless
Communications for Diversity Combining and Log-Likelihood Scaling,"
filed Jan. 28, 2005, now U.S. Pat. No. 7,672,383 which claims the
benefit of priority from U.S. Provisional Patent Application No.
60/611,028, entitled "Noise Variance Estimation for Diversity
Combining and Log-likelihood Ratio (LLR) Scaling in Platinum
Broadcast" filed Sep. 17, 2004, both of which are assigned to the
assignee hereof.
Claims
What is claimed is:
1. A demodulator, comprising; a discrete fourier transform
configured to convert a symbol from a time domain to a frequency
domain; a pilot tone filter operably connected to said discrete
fourier transform, wherein said pilot tone filter is configured to
select pilot tones; a data tone filter having a first input
operably connected to a first output of said discrete fourier
transform and a second input operably connected to a first output
of said pilot tone filter; a signal demapper having a first input
operably connected to an output of said data tone filter, wherein
said data tone filter is configured to pass data from said discrete
fourier transform to said signal demapper and said signal demapper
is configured make a soft decision based on received data and an
estimate of a channel frequency response; and a channel estimator
having an input operably connected to a second output of said pilot
tone filter.
2. The demodulator according to claim 1, wherein said pilot tone
filter is also configured to select guard tones.
3. The demodulator according to claim 1, wherein said channel
estimator is configured to generate channel estimates for in-band
and band-edge said pilot tones.
4. The demodulator according to claim 1, wherein said channel
estimator is configured to generate channel estimates for said
pilot tones using least-squares channel estimation.
5. The demodulator according to claim 1, wherein said channel
estimator is configured to provide an estimate of said channel's
frequency response.
6. The demodulator according to claim 1, wherein said channel
estimator comprises: an inverse discrete fourier transform
configured to convert pilot tones into estimates of a channel
impulse response; and a second discrete fourier transform operably
connected to said inverse discrete fourier transform.
7. The demodulator according to claim 3, wherein said channel
estimator comprises: an inverse discrete fourier transform
configured to convert pilot tones into estimates of a channel
impulse response; and a second discrete fourier transform operably
connected to said inverse discrete fourier transform.
8. The demodulator according to claim 5, wherein said symbols are
OFDM symbols and wherein said channel estimate is time averaged for
said OFDM symbols in a time-slot.
9. The demodulator according to claim 6, wherein said second
discrete fourier transform is configured to estimate said channel
frequency response from said channel impulse response for all tones
using interpolation.
10. The demodulator according to claim 7, wherein said symbols are
OFDM symbols, wherein said channel estimate is time averaged for
said OFDM symbols in a time-slot and wherein said second discrete
fourier transform is configured to estimate said channel frequency
response from said channel impulse response for tones using
interpolation.
11. A method of demodulating symbols, the method comprising;
converting, at a processor, a symbol from a time domain to a
frequency domain to generate a converted symbol; selecting pilot
tones using the converted symbol; receiving a signal and the
converted symbol at a data tone filter, wherein the signal is
generated based on the pilot tones; estimating a channel frequency
response using the selected pilot tones; and making a soft decision
based on received data and the estimate of the channel frequency
response.
12. The method of demodulating according to claim 11, further
comprising selecting guard tones.
13. The method of demodulating symbols according to claim 11,
further comprising generating channel estimates for in-band and
band-edge said pilot tones.
14. The method of demodulating symbols according to claim 11,
further comprising generating channel estimates for said pilot
tones using least-squares channel estimation.
15. The method of demodulating symbols according to claim 11,
further comprising providing an estimate of a channel's frequency
response.
16. The method of demodulating symbols according to claim 11,
further comprising converting said pilot tones into estimates of a
channel impulse response.
17. The method of demodulating symbols according to claim 13,
further comprising converting said pilot tones into estimates of a
channel impulse response.
18. The method of demodulating symbols according to claim 15,
wherein said symbols are OFDM symbols and further comprising time
averaging said channel estimate for said OFDM symbols in a
time-slot.
19. The method of demodulating symbols according to claim 16,
further comprising estimating said channel frequency response from
said channel impulse response for all tones using
interpolation.
20. The method of demodulating symbols according to claim 17,
wherein said symbols are OFDM symbols and further comprising: time
averaging said channel estimate for said OFDM symbols in a
time-slot; and estimating said channel frequency response from said
channel impulse response for tones using interpolation.
21. An apparatus for demodulating symbols, comprising: means for
converting a symbol from a time domain to a frequency domain; means
for selecting pilot tones, wherein the means for selecting the
pilot tones is operably coupled to the means for converting the
symbol from the time domain to the frequency domain; means for
filtering data tones having a first input operably coupled to a
first output of the means for converting the symbol from the time
domain to the frequency domain and having a second input operably
coupled to a first output of the means for selecting pilot tones;
means for estimating a channel frequency response having an input
operably coupled to a second output of the means for selecting
pilot tones; and means for making a soft decision having a first
input operably coupled to an output of the means for filtering data
tones, wherein the means for filtering data tones is configured to
pass data from the means for converting the symbol from the time
domain to the frequency domain to the means for making a soft
decision and the means for making a soft decision is configured
make a soft decision based on received data and the estimate of the
channel frequency response.
22. The apparatus for demodulating according to claim 21, further
comprising means for selecting guard tones.
23. The apparatus for demodulating symbols according to claim 21,
further comprising means for generating channel estimates for
in-band and band-edge said pilot tones.
24. The apparatus for demodulating symbols according to claim 21,
further comprising means for generating channel estimates for said
pilot tones using least-squares channel estimation.
25. The apparatus for demodulating symbols according to claim 21,
further comprising means for providing an estimate of a channel's
frequency response.
26. The apparatus for demodulating symbols according to claim 21,
further comprising means for converting said pilot tones into
estimates of a channel impulse response.
27. The apparatus for demodulating symbols according to claim 23,
further comprising means for converting said pilot tones into
estimates of a channel impulse response.
28. The apparatus for demodulating symbols according to claim 25,
wherein said symbols are OFDM symbols and further comprising means
for time averaging said channel estimate for said OFDM symbols in a
time-slot.
29. The apparatus for demodulating symbols according to claim 26,
further comprising means for estimating said channel frequency
response from said channel impulse response for all tones using
interpolation.
30. The apparatus for demodulating symbols according to claim 27,
wherein said symbols are OFDM symbols and further comprising: means
for time averaging said channel estimate for said OFDM symbols in a
time-slot; and means for estimating said channel frequency response
from said channel impulse response for tones using
interpolation.
31. A computer program product, comprising a non-transitory
computer-readable medium comprising executable code for causing a
computer to: convert a symbol from a time domain to a frequency
domain to generate a converted symbol; select pilot tones using the
converted symbol; receiving signaling and the converted symbol at a
data tone filter, wherein the signaling is generated based on the
pilot tones; estimate a channel frequency response using the
selected pilot tones; and make a soft decision based on received
data and the estimate of the channel frequency response.
32. The computer program product according to claim 31, further
comprising code to select guard tones.
33. The computer program product according to claim 31, further
comprising code to generate channel estimates for in-band and
band-edge said pilot tones.
34. The computer program product according to claim 31, further
comprising code to generate channel estimates for said pilot tones
using least-squares channel estimation.
35. The computer program product according to claim 31, further
comprising code to provide an estimate of a channel's frequency
response.
36. The computer program product according to claim 31, further
comprising code to convert said pilot tones into estimates of a
channel impulse response.
37. The computer program product according to claim 33, further
comprising code to convert said pilot tones into estimates of a
channel impulse response.
38. The computer program product according to claim 35, wherein
said symbols are OFDM symbols and further comprising code to time
average said channel estimate for said OFDM symbols in a
time-slot.
39. The computer program product according to claim 36, further
comprising code to estimate said channel frequency response from
said channel impulse response for all tones using
interpolation.
40. The computer program product according to claim 37, wherein
said symbols are OFDM symbols and further comprising: code to time
average said channel estimate for said OFDM symbols in a time-slot;
and estimate said channel frequency response from said channel
impulse response for tones using interpolation.
Description
BACKGROUND
1. Field
The present disclosure relates generally to telecommunications, and
more specifically, to noise variance estimation techniques in
wireless communications.
2. Background
In a typical telecommunications system, the data to be transmitted
is encoded with a turbo code, which generates a sequence of
symbols, referred to as "code symbols." Several code symbols may be
blocked together and mapped to a point on a signal constellation,
thereby generating a sequence of complex "modulation symbols." This
sequence may be applied to a modulator, which generates a
continuous time signal, which is transmitted over a wireless
channel.
At the receiver, the modulation symbols may not correspond to the
exact location of a point in the original signal constellation due
to noise and other disturbances in the channel. A demodulator may
be used to make soft decisions as to which modulation symbols were
most likely transmitted based on the received points in the signal
constellation. The soft decisions may be used to extract the
Log-Likelihood Ratio (LLR) of the code symbols. The turbo decoder
uses the sequence of code symbol LLRs to decode the data originally
transmitted.
In a receiver employing multiple antennas, a Pilot Weighted
Combining (PWC) technique is often used to combine the soft
decisions for each antenna. The combined soft decisions may then be
used to compute the LLRs for the code symbols. One problem with
this approach is the potential difference in thermal noise for each
antenna. As a result, the PWC procedure for combining soft
decisions may not optimize the Signal-to-Noise Ratio (SNR).
Accordingly, there is a need in the art for an improved
demodulation process that considers the thermal noise for one or
more antennas mounted on a receiver.
SUMMARY
In view of the above, the described features of the present patent
application generally relate to one or more improved systems,
methods and/or apparatuses for demodulating symbols.
In one example, the present patent application comprises an OFDM
demodulator, comprising a discrete fourier transform configured to
convert an OFDM symbol from a time domain to a frequency domain, a
pilot tone filter operably connected to the discrete fourier
transform, wherein the pilot tone filter is configured to select
pilot tones, a data tone filter having a first input operably
connected to a first output of the discrete fourier transform and a
second input operably connected to a first output of the pilot tone
filter, a signal demapper having a first input operably connected
to an output of the data tone filter, wherein the data tone filter
is configured to pass data from the discrete fourier transform to
the signal demapper and the signal demapper is configured make a
soft decision based on received data and an estimate of a channel
frequency response; and a channel estimator having an input
operably connected to a second output of the pilot tone filter.
In another example, the pilot tone filter is also configured to
select guard tones.
In another example, the channel estimator is configured to generate
channel estimates for in-band and band-edge pilot tones.
In another example, the channel estimator is configured to generate
channel estimates for said pilot tones using least-squares channel
estimation.
In another example, the channel estimator is configured to provide
an estimate of said channel's frequency response.
In another example, the channel estimator comprises an inverse
discrete fourier transform configured to convert pilot tones into
estimates of a channel impulse response, and a second discrete
fourier transform operably connected to the inverse discrete
fourier transform.
In another example, the channel estimate is time averaged for said
OFDM symbols in a time-slot.
In another example, the second discrete fourier transform is
configured to estimate the channel frequency response from the
channel impulse response for all tones using interpolation.
In another example, the present patent application comprises a
method and means for demodulating symbols, comprising converting an
OFDM symbol from a time domain to a frequency domain, selecting
pilot tones, making a soft decision based on received data, and
estimating a channel frequency response.
In another example, the method and means further comprises
selecting guard tones.
In another example, the method and means further comprises
generating channel estimates for in-band and band-edge pilot
tones.
In another example, the method and means further comprises
generating channel estimates for the pilot tones using
least-squares channel estimation.
In another example, the method and means further comprises
providing an estimate of a channel's frequency response.
In another example, the method and means further comprises
converting the pilot tones into estimates of a channel impulse
response.
In another example, the method and means further comprises time
averaging said channel estimate for the OFDM symbols in a
time-slot.
In another example, the method and means further comprises
estimating the channel frequency response from the channel impulse
response for all tones using interpolation.
It is understood that other embodiments of the present invention
will become readily apparent to those skilled in the art from the
following detailed description, wherein various embodiments of the
invention are shown and described by way of illustration. As will
be realized, the invention is capable of other and different
embodiments and its several details are capable of modification in
various other respects, all without departing from the spirit and
scope of the present invention. Accordingly, the drawings and
detailed description are to be regarded as illustrative in nature
and not as restrictive.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a conceptual block diagram illustrating an example of a
telecommunications system;
FIG. 2 is a conceptual block diagram illustrating an example of a
transmitter in communication with a receiver;
FIG. 3 is an example of a transmission waveform for a hybrid
multi-access telecommunications system supporting both CDMA and
OFDM communications;
FIG. 4 is a conceptual block diagram illustrating the functionality
of an OFDM demodulator in a receiver for a hybrid multi-access
telecommunications system;
FIG. 5 is a conceptual block diagram illustrating the functionality
of an OFDM demodulator in a dual antenna receiver for a hybrid
multi-access telecommunications system;
FIG. 6 is a graphical illustration of an OFDM symbol in the
frequency domain;
FIG. 7 is a conceptual block diagram illustrating the functionality
of a channel estimator capable of computing the effective noise
variance for its respective antenna; and
FIG. 8 is a flow diagram illustrating a method of estimating an
effective noise variance for the band-edge tones.
DETAILED DESCRIPTION
The detailed description set forth below in connection with the
appended drawings is intended as a description of various
embodiments of the present invention and is not intended to
represent the only embodiments in which the present invention may
be practiced. The detailed description includes specific details
for the purpose of providing a thorough understanding of the
present invention. However, it will be apparent to those skilled in
the art that the present invention may be practiced without these
specific details. In some instances, well-known structures and
components are shown in block diagram form in order to avoid
obscuring the concepts of the present invention.
FIG. 1 is a conceptual block diagram illustrating an example of a
telecommunications system. The telecommunications system 100 may
include an Access Network (AN) 102 which supports communications
between any number of ATs 104. The AN 102 may also be connected to
additional networks 110A and 1110B outside the AN 102, such as the
Internet, a corporate intranet, a Public Switched Telephone Network
(PSTN), a broadcast network, or any other network. The Access
Terminal (AT) 104 may be any type of fixed or mobile device that
can communicate with the AN 102 including but not limited to a
wireless handset or telephone, a cellular telephone, a data
transceiver, a paging receiver, a position determination receiver,
a modem, or the any other wireless terminal.
The AN 102 may be implemented with any number of base stations
dispersed throughout a geographic region. The geographic region may
be subdivided into smaller regions known as cells with a base
station serving each cell. In high traffic applications, the cell
may be further divided into sectors with a base station serving
each sector. For simplicity, one Base Station (BS) 106 is shown. A
Base Station Controller (BSC) 108 may be used to coordinate the
activities of multiple base stations, as well as provide an
interface to the networks outside the AN 102.
FIG. 2 is a conceptual block diagram illustrating an example of a
transmitter in communication with a receiver. The transmitter 202
and receiver 204 may be stand-alone entities, or integrated into a
telecommunications system. In a telecommunications system, the
transmitter 202 may be in the base station 106 and the receiver 204
may be in the AT 104. Alternatively, the transmitter 202 may be in
the AT 104 and the receiver 204 may be in the base station 106.
At the transmitter 202, a Turbo encoder 206 may be used to apply an
iterative coding process to the data to Facilitate Forward Error
Correction (FEC). The coding process results in a sequence of code
symbols with redundancy used by the receiver 204 to correct errors.
The code symbols may be provided to a modulator 208 where they are
blocked together and mapped to coordinates on a signal
constellation. The coordinates of each point in the signal
constellation represents the baseband quadrature components that
are used by an analog front end 210 to modulate quadrature carrier
signals before transmission over a wireless channel 212.
An analog front end 214 in the receiver 204 may be used to convert
the quadrature carrier signals to their baseband components. A
demodulator 21 (may translate the baseband components back to their
correct points in the signal constellation. Because of noise and
other disturbances in the channel 212, the baseband components may
not correspond to valid locations in the original signal
constellation. The demodulator 216 detects which modulation symbols
were most likely transmitted by correcting the received points in
the signal constellation by the channel's frequency response, and
selecting valid symbols in the signal constellation which are
closest to the corrected received points. These selections are
referred to as "soft decisions." Soft decisions are used by LLR
computation module 218 to determine the LLR of the code symbols. A
turbo decoder 220 uses the sequence of code symbol LLRs to decode
the data originally transmitted.
The telecommunications system may be implemented with any number of
different technologies. Code Division-Multiple Access (CDMA), which
is well known in the art, is just one example. CDMA is a modulation
and multiple access schemes based on spread-spectrum
communications. In a CDMA telecommunications system, a large number
of signals share the same frequency spectrum; as a result, such as
system provides high user capacity. This is achieved by
transmitting each signal with a different code, and thereby,
spreading the spectrum of the signal waveform. The transmitted
signals are separated in the receiver by a demodulator that uses a
corresponding code to despread the signal. The undesired signals,
i.e. signals having a different code, are not despread and
contribute to noise.
Orthogonal Frequency Division Multiplexing (OFDM) is another
example of a technology that can be implemented by a
telecommunications system. OFDM is a spread-spectrum technique
wherein data is distributed over a large number of carriers spaced
apart at precise frequencies. The spacing provides "orthogonality"
to prevent a receiver from seeing frequencies other than those
intended for the receiver. OFDM, which is also well known in the
art, is commonly used for commercial and private broadcasts, but is
not limited to such applications.
In at least one embodiment of the telecommunications system, a
hybrid multi-access scheme may be employed using both CDMA and OFDM
communications. This hybrid system has been gaining widespread
acceptance in the area of broadcast services integrated into
existing infrastructures, wherein such infrastructures were
originally designed to support point-to-point communications
between a transmitter and receiver. In other words, the one-to-one
type communication system is also being used for one-to-many
broadcast transmissions by use of OFDM modulation in combination
with other technologies. In these systems, the transmitter may be
used to puncture OFDM symbols into a CDMA waveform.
FIG. 3 is an example of a transmission waveform for a hybrid
multi-access telecommunications system supporting both CDMA and
OFDM communications. The structure of the transmission waveform, as
well as the specified time durations, chip lengths, and value
ranges are provided by way of example with the understanding that
other time durations, chip lengths, and value ranges may be used
without departing, from the underlying principles of operation of
the telecommunications system. The term "chip" is referred to
herein as a unit of time of a binary digit output by a
spread-spectrum code generator. This example is consistent with a
system supporting the protocol "cdma2000 High Rate Packet Data Air
Interface Specification," TIA/EIA/IS-856.
The transmission waveform 300 may be defined in terms of frames. A
frame may include 16 time-slots 302, each time-slot 302
corresponding to 2048 chips. Time slot 302 having a 1.66
millisecond (ins) time-slot duration, and consequently, a 26.66 ms
frame duration. Each time-slot 302 may be divided into two
half-time-slots 302A, 302B, with CDMA pilot tone bursts 304A, 304B
transmitted within each half-time-slot 302A, 302B, respectively.
Each CDMA pilot tone burst 304A, 304B may be 96 chips, centered
about a mid-point of its associated half-time-slot 302A, 302B. A
Medium Access Control (MAC) channel 306A, 306B, 306C, 306D may
comprise two bursts, which are transmitted immediately before and
immediately after the pilot tone burst 304A, 304B of each
half-time-slot 302A, 302B. The MAC may include up to 64
spread-spectrum code channels, which are orthogonally covered by
64-ary Walsh codes. The MAC channels may be used for CDMA overhead
such as power control, data rate control, and the like. Data may be
sent in the remaining portions 308A, 308B of the first
half-time-slot 302A and the remaining portions 308C, 308D of the
second half-time-slot 302B.
In one embodiment of a hybrid telecommunications system, four OFDM
symbols may be punctured into the data portion of a time-slot 302.
This results in a zeroth OFDM symbol 308A at the beginning of the
first half-time-slot 302A, a first OFDM symbol 308B at the end of
the first half-time-slot 302A, a second OFDM 308C symbol at the
beginning of the second half-time-slot 302B, and a third OFDM
symbol at the end of the second half-time-slot 302B. In this
example, each OFDM symbol is 400 chips. A cyclic prefix 310
occupies 80 chips, leaving 320 chips to transmit data and pilot
tones. The 320 chips translates into 320 equally spaced orthogonal
tones across the frequency band. Because the tones at the edges of
the frequency band may be affected by Adjacent Channel Interference
(ACI), the skilled artisan may chose not to send any data on those
tones. Instead, the edges of the frequency band, referred to as
"guard-bands," may be used to transmit "pilot tones" and "guard
tones." The tones that are not affected by ACI are typically used
to transmit modulation symbols with interspersed pilot tones. Both
the guard tones and pilot tones are modulated with known data.
Depending on the application, the guard tones and the pilot tones
may be the same or different.
FIG. 4 is a conceptual block diagram illustrating the functionality
of an OFDM demodulator in a receiver for a hybrid multi-access
telecommunications system. The OFDM demodulator 402 may be
integrated into any processing entity, or distributed among any
number of processing entities, within the receiver. The processing
entity (or entities) may include a microprocessor, Digital Signal
Processor (DSP), or any other hardware and/or software based
processing entity (or entities). Alternatively, the OFDM
demodulator 402 may be a separate processing entity such as a
microprocessor, DSP, programmable logic, dedicated hardware, or any
other entity capable of processing information.
The OFDM demodulator 402 may include a Discrete Fourier Transform
(DFT) 404, which may be used to process OFDM symbols. The DFT 402
may be used to convert an OFDM symbol from the time domain to the
frequency domain. The output of the DFT 404 may be provided to a
pilot tone filter 406 in a serial fashion. The pilot tone filter
406 may be implemented as a decimator to select the pilot tones.
The decimator may also be configured to select all guard tones.
Signaling from the pilot tone filter 406 to a data tone filter 407
may be used to indicate when the data tone filter 407 should pass
data from the DFT 404 to a signal demapper 410. The signal demapper
410 makes a soft decision as to the modulation symbol in the signal
constellation most likely transmitted on the data tone. This
decision is based on received data and an estimate of the channel's
frequency response provided by a channel estimator 408. The channel
estimator 408 may estimate the channel's frequency response from
the pilot tones using a least-squares channel estimation procedure,
or any other suitable procedure.
The channel estimator 408 may be implemented with an Inverse
Discrete Fourier Transform (IDFT) 412. The IDFT 412 converts the
pilot tones from the frequency domain into the estimate of the
channel impulse response of length P samples in the time domain,
where P is the number of pilot tones in the OFDM symbol. The
channel's frequency response may then be estimated for all tones
from the estimate of the channel impulse response using an
interpolation process implemented by a DFT 414. The number of
samples used by the DFT 414 to compute the channel estimate may be
reduced if the actual channel's impulse response is less than PT,
where l/T is equal to the chip rate of the OFDM symbol. In this
case, the channel's frequency response may be estimated from L
samples, where LT is equal to the time duration of the channel's
impulse response. The term L is generally referred to as the "delay
spread" of the channel impulse response.
The channel estimate may be improved by time-averaging the channel
estimates for all OFDM symbols in any given time-slot. In the
example discussed in FIG. 3, four channel estimates from four ODFM
symbols may be time-averaged. Ideally, a non-causal symmetric
filter should be used to time-average the channel estimates for the
four ODFM symbols. By way of example, the channel estimate for the
first OFDM symbol 308B may be computed by averaging the channel
estimates for the zeroth, first, and second OFDM symbols 308A,
308B, 308C. Similarly, the channel estimate for the second OFDM
symbol 308C may be computed by averaging the first, second, and
third OFDM symbols 308B, 308C, 308D. This approach minimizes the
channel estimation bias caused by channel variation induced by
Doppler. However, for the zeroth and third OFDM symbols 308A, 308D,
this is not possible because adjacent time-slots may contain CDMA
signals. Hence, a non-causal filter cannot be applied to the zeroth
and third OFDM symbols 308A, 308D. Instead, the channel estimate
for the zeroth OFDM symbol 308A may be computed by a weighted
averaging process between the zeroth and first OFDM symbols 308A,
308B, and the channel estimate for the third OFDM symbol 308D may
be computed by a weighted averaging process between the second and
third OFDM symbols 308C, 308D. Alternatively, the channel estimate
for the zeroth OFDM symbol 308A may be computed by a weighted
averaging process between the zeroth, first, and second OFDM
symbols 308A, 308B, 308C, and the channel estimate for the third
OFDM symbol 308D in the time-slot may be computed by a weighted
averaging process between the first, second and third OFDM symbols
308B, 308C, 308D. The latter approach, however, may cause
significant channel estimation bias at high mobile speeds. Either
way, the channel estimates for the first and second OFDM symbols
308B, 308C in the time-slot should be more accurate than the
channel estimates for the zeroth and third OFDM symbols 308a, 308d
in the same time-slot.
In multiple antenna applications employing diversity combining
techniques, a sequence of soft decisions may be generated for each
antenna. The soft decisions for any given tone (k) may be combined
using a Maximum Ratio Combining (MRC) technique before being
provided to the LLR computation module. The MRC technique scales
each soft decision for a given tone by 1/.sigma..sub.eff,k.sup.(m)2
for the m.sup.th antenna, where the effective noise variance
(.sigma..sub.eff,k.sup.(m)2) is defined by the following equation:
.sigma..sub.eff,k.sup.(m)2=.sigma..sub..DELTA.,k.sup.(m)2+.sigma..sub.k.s-
up.(m)2 (1) where: .sigma..sub..DELTA.,k.sup.(m)2 is the
Mean-Square Error (MSE) of the channel estimate for the k-th tone
received by the m.sup.th antenna; and .sigma..sub.k.sup.(m)2 is the
noise variance of the k.sup.th tone received by the m.sup.th
antenna.
FIG. 5 is a conceptual block diagram illustrating the functionality
of an OFDM demodulator in a dual antenna receiver for a hybrid
multi-access telecommunications system. The OFDM demodulator 502
may be implemented in a stand-alone processing entity, distributed
among multiple processing entities, or integrated into another
receiver entity in the same manner as the OFDM modulator described
in connection with FIG. 4. The OFDM demodulator 502 is shown with
two demodulating channels 502A, 502B, one for each antenna, but may
be implemented with any number of demodulating channels depending
on the number of antennas in the receiver. In this example, a noise
variance estimator 504A, 504B in each demodulating channel 502A,
502B, respectively, estimates the effective noise variance
.sigma..sub.eff,k.sup.(m)2 for each tone. The soft decisions
generated by each signal demapper 410A, 410B are provided to a
scaler 506A, 506B, where they are scaled by
1/.sigma..sub.eff,k.sup.(m)2 before being combined with other
scaled soft decisions by an adder 508.
FIG. 6 is a graphical illustration of an OFDM symbol in the
frequency domain. As discussed earlier in connection with FIG. 3,
each OFDM symbol may include guard-bands 602A, 602B containing only
pilot and guard tones. The tones not affected by ACI are typically
used to transmit modulation symbols with interspersed pilot tones;
however, a tone not affected by ACI, may still have a channel
estimate which is affected by ACI. This is because the channel
estimate is computed from the interpolation of multiple pilot
tones, and in some cases those pilot tones may extend into the
guard-band regions. Those tones outside the guard-band regions
whose channel estimate are affected by ACI, as well as the tones in
the guard-band regions, will be referred to as "band-edge tones."
These tones can be found in the band-edge regions 604A, 604B of the
frequency band for the OFDM symbol. The remaining tones, with
channel estimates that are not affected by ACI, will be referred to
as "in-band tones," and may be found in the in-band region 606 of
the OFDM symbol.
FIG. 7 is a conceptual block diagram illustrating the functionality
of a channel estimator capable of computing the effective noise
variance for its respective antenna. A noise variance estimator 504
may be used to perform this computation. The noise variance
estimator 504 may be implemented as part of the channel estimator
408, may be a stand-alone entity, may be implemented as part of
another processing entity within the receiver, or may have its
functionality distributed among any number of processing entities
in the receiver.
The noise variance estimator 504 may include an in-band estimator
702 configured to compute the effective noise variance for the
in-band tones, and a band-edge estimator 704 configured to compute
the effective noise variance for the band-edge tones. The output at
702 and the output of 704 are provided to a multiplexer (MUX) 703
or a switch. The output of the MUX 703 is then provided to scaler
506. The effective noise variance for in-band tones may be computed
from the in-band pilot tones and the channel estimates for the
in-band pilot tones. The effective noise variance for the band-edge
tones may be computed from the band-edge pilot tones and the
channel estimates for the band-edge pilot tones. The accuracy of
the effective noise variance for the band-edge tones may be
improved by also using the guard-band tones.
The operation of the in-band estimator will first be discussed. The
in-band tones are the tones for which the MSE of the channel
estimates are related to the noise variance of the tones by the
following equation:
.sigma..DELTA..times..function..apprxeq..times..times..times..sigma..time-
s. ##EQU00001## where c.sub.n,l is the time-averaging weights for
the channel estimate of the n.sup.th OFDM symbol, and
.sigma..sup.(m)2 is the noise variance of the tones received by the
m.sup.th antenna, which are not affected by ACI. The tone index, or
the subscript k, may be suppressed because the noise variance can
be assumed to be the same for all the in-band tones.
Thus, the effective noise variance is related to the noise variance
by the following equation:
.sigma..times..function..times..times..times..sigma..times.
##EQU00002## The noise variance .sigma..sup.(m)2 may be computed
and scaled using equation (3) to generate the effective noise
variance .sigma..sub.eff..sup.(m)2 (n).
A set of in-band pilot tones may be defined as .LAMBDA.={k;
-(P-G)/2.ltoreq.k.ltoreq.(P-G)/2}, where G>0 is such that the
MSE of the time-averaged channel estimates for the k-th pilot tone
can be represented by the following equation:
.sigma..DELTA..times..times..delta..times..function..apprxeq..times..time-
s..times..sigma..times..times..times..times..di-elect
cons..LAMBDA..times..times..times..times. ##EQU00003## where
.delta.=N/P is the pilot tone spacing, N is the number of
orthogonal tones, P is the number of pilot tones, and (G-1) is the
number of pilot tones whose channel estimates are affected by
ACI.
There are four sets of time-averaging weights for the channel
estimation; (c.sub.0.0,c.sub.0.1,c.sub.0.2,c.sub.0.3) for the
zeroth OFDM symbol, (c.sub.1.0,c.sub.1.1,c.sub.1.2,c.sub.1.3) for
the first OFDM symbol, (c.sub.2.0,c.sub.2.1,c.sub.2.2,c.sub.2.3)
for the second OFDM symbol, and
(c.sub.3.0,c.sub.3.1,c.sub.3.2,c.sub.3.3) for the third OFDM
symbol: The estimator for the in-band effective noise variance for
the n.sup.th OFDM symbol is given by:
.sigma..times..function..times..times..times..times..times..times..times.-
.di-elect cons..LAMBDA..times. ##EQU00004##
where: w.sub.l are the combining weights such that the mean of
.times..times. ##EQU00005## is .sigma..sup.(m)2; Y.sub.k,l.sup.(m)
is the pilot observation corresponding to the k.sup.th pilot tone
of the l.sup.th OFDM symbol; and H.sub.k,l.sup.(m) is the channel
estimate for the k.sup.th pilot tone of the l.sup.th OFDM
symbol.
An example will be illustrative. In this example, the noise
variance estimator will use only the first and second OFDM symbols
to estimate the noise variance, which can be represented as
follows:
.times..times..times..times..times..times..times..times..times..times..ti-
mes..times. ##EQU00006##
It can be shown that the mean of
|Y.sub.k,l.sup.(m)-H.sub.k,l.sup.(m)|.sup.2 is
.times..times..times..times..times..times..sigma..times.
##EQU00007## Thus, the mean of f.sub.l.sup.(m) is
.times..times..times..times..times..times..times..sigma..times.
##EQU00008## because there are P-G-1 in-band pilot tones per OFDM
symbol, and using the weights w.sub.l, the mean of
w.sub.lf.sub.l.sup.(m) becomes 1/2.sigma..sup.(m)2.
In the example algorithm, only the first and second OFDM symbols
are used for the channel estimates. Thus, the mean of the effective
noise variance may be represented as follows:
.times..times..times..times..sigma..times..times..sigma..times..times..ti-
mes..times..sigma..times. ##EQU00009##
The weights were designed for the case when the first and second
OFDM symbols use the same non-causal symmetric time-averaging
weights, i.e.
(c.sub.1.0,c.sub.1.1,c.sub.1.2,c.sub.1.3)=(1/3,1/3,1/3,0), and
(c.sub.2.0,c.sub.2.1,c.sub.2.2,c.sub.2.3)=(0,1/3,1/3,1/3). However,
the zeroth and third symbols use different time-averaging filters,
e.g., (c.sub.0.0,c.sub.0.1,c.sub.0.2,c.sub.0.3)=(2/3,1/3,0,0), and
(c.sub.3.0,c.sub.3.1,c.sub.3.2,c.sub.3.3)=(0,0,1/3,2/3). In this
case, the time-averaged channel estimates for the zeroth and third
OFDM symbols may have large bias due to the time-variation of the
channel at high mobile speed. As a result, the condition
.sigma..DELTA..times..function..apprxeq..times..times..times..sigma..time-
s. ##EQU00010## may no longer be satisfied. Hence, the channel
estimates for only first and second OFDM symbols are used in this
example.
Alternatively, the channel estimate may be based on only one OFDM
symbol. In this case, the effective noise variance can be estimated
as follows:
.sigma..times..function..times..times..times..times..times..times..times.-
.times..times..times..times. ##EQU00011##
The mean of the effective noise variance is the same as before.
However, the variance is larger than that using two OFDM symbols.
In other words, the former is less accurate than the latter.
The accuracy of the effective noise variance may be improved by
using the zeroth and third OFDM symbols, but the channel estimates
H.sub.k,0.sup.(m) and H.sub.k,3.sup.(m) used in f.sub.0.sup.(m) and
f.sub.3.sup.(m) are without time-averaging, i,e. (c.sub.0.0,
c.sub.0.1, c.sub.0.2, c.sub.0.3)=(1,0,0,0), and
(c.sub.3.0,c.sub.3.1,c.sub.3.2,c.sub.3.3)=(0,0,0,1). In this case,
the weights may be represented as follows:
.times..times..times..times..times..times..times..times..times..times..ti-
mes. ##EQU00012##
In sum, the in-band estimator may be used to compute
f.sub.l.sup.(m), or the sum of
|Y.sub.k,l.sup.(m)-H.sub.k,j.sup.(m)|.sup.2 of in-band tones, to
get an estimate of
.times..times..times..times..times..times..times..sigma..times.
##EQU00013## which is proportional to the noise variance
.sigma..sup.(m)2 of the in-band tones. Combining weights may then
be chosen so that the mean of the result is the same as
.sigma..sub.eff..sup.(m)2(n) for each OFDM symbol (n=0, 1, 2, 3),
i.e., E[{circumflex over
(.sigma.)}.sub.eff.sup.(m)2(n)]=.sigma..sub.eff..sup.(m)2(n). (E[X]
denotes expectation or mean of random variable X.) Because
different time-averaging weights c.sub.n,l for each OFDM
symbol,
.times..times. ##EQU00014## may also be different for each symbol.
This may cause the different tones in different OFDM symbols in the
same time-slot to have different effective noise variances. This
should be compensated for in the LLR calculation by the term
.times..times. ##EQU00015##
The band-edge estimator will now be discussed. As discussed
earlier, in-band tones and the band-edge tones may be determined by
comparing the MSE of the channel estimate for the k-th tone
.sigma..sub..DELTA.,k.sup.(m)2(n) with
.times..times..times..times..sigma..times. ##EQU00016## where
.sigma..sup.(m)2 is the noise variance of the tones which are not
affected by ACI. If they are close to each other, the tones are
classified as in-band tones. Otherwise, they are classified as
band-edge tones. Given the delay spread L, the number of pilot
tones P, and the characteristics of the ACI, such as the adjacent
carrier spacing and its power relative to .sigma..sup.(m)2, the
relation between the MSE of the channel estimate for the k-th tone
.sigma..sub..DELTA.,k.sup.(m)2(n) and the noise variance
.sigma..sup.(m)2 may be determined either through mathematical
analysis or simulations. This may be done in the system design
phase, before the noise variance estimator is integrated into the
receiver of an AT, and then stored in memory.
A set of band-edge pilot tones may be represented as .LAMBDA.={k;
(P-G)/2.ltoreq.k.ltoreq.P/2-1 or -P/2.ltoreq.k.ltoreq.(P-G)/2-1)},
where G-1 is the number of band-edge pilot tones and k is the pilot
tone index. This set may be determined in the system design phase,
and stored in memory.
An example will be illustrative. In this example, N=320. So the
tone index k goes from -160 to 159, (i.e., k=-160, -159, -158, . .
. -1, 0, 1 . . . 158, 159). There are 64 pilot tones (i.e., P=64),
and 15 band-edge pilot tones (i.e., G=16). The pilot tones are
spaced apart by five frequency tones (i.e., tone indices: k=-160,
-155, . . . -5, 0, 5, . . . 150, 155.). Based on these conditions,
the in-band tones may be represented by -120.ltoreq.k.ltoreq.120,
the in-band pilot tones may be represented by the pilot tone
indices -24.ltoreq.k.ltoreq.24, the band-edge tones may be
represented by tone indices 121.ltoreq.k.ltoreq.159 and
-160.ltoreq.k.ltoreq.-121, the band-edge pilot tones may be
represented by the pilot tone indices 25.ltoreq.k.ltoreq.31 and
-32.ltoreq.k.ltoreq.-25, and the guard-band tones may be
represented by tone indices 150.ltoreq.k.ltoreq.159 and
-160.ltoreq.k.ltoreq.-151. But the pilot tones are punctured in the
guard tones, and as a result, the tones at k=-160, -155, 150, 155
are pilot tones. Accordingly, there are K=20-4=16 guard tones.
There are 241 in-band tones and 79 band-edge tones. So the majority
of the tones are in-band tones. This example also shows the data
sent on some band-edge tones.
The noise variance of a band-edge tone is the sum of the noise
variance of the in-band tones and the variance of the ACI for the
band-edge tones. The MSE of the channel estimate for a band-edge
tone is the sum of the MSE of the channel estimate for the in-band
tones and the component due to ACI. In general, the amount of the
adjacent channel interference in each band-edge tone is different
from tone to tone. Hence, it is difficult to accurately estimate
the effective noise variances for band-edge tones. However,
accounting for the fact that there is ACI in the noise variance
estimates, it is possible to improve performance. This is achieved
by de-emphasizing the LLR's computed from the tones affected by
ACI.
The noise variance estimator may be designed such that, in the
absence of ACI, the following equation is satisfied:
.times..sigma..times..function..times..times..times..sigma..times.
##EQU00017## In other words, if there is no ACI, the mean of the
noise variance estimator should be the same as the effective noise
variance.
The noise variance estimator may be used to account for the
increase in the effective noise variance due to the ACI. This may
be achieved by using the band-edge tones and guard tones to
estimate the effective noise variance. The mean of the estimate
will not be the same as the effective noise variance. However, it
will be larger than the in-band noise variance estimate. Hence, the
band-edge tones will be de-emphasized in LLR computation.
The following band-edge estimator algorithm may be used. The
algorithm may be used to compute the average of the variances of
the band-edge tones as follows:
.sigma..times..function..times..times..times..times..lamda..times..times.-
.mu..times..times..times..times..di-elect
cons..LAMBDA..times..times..times..di-elect cons..OMEGA..times.
##EQU00018## where: .OMEGA. is a set of tone indices for the guard
tones; X.sub.k,l.sup.(m) is the k-th tone for the l-th OFDM symbol:
Y.sub.k,l.sup.(m)=X.sub.k.delta.,l.sup.(m), where .delta.=N/P is a
pilot tone spacing. By way of example, the first pilot tone is the
fifth tone of the OFDM symbol, so
Y.sub.1,l.sup.(m)=X.sub.5,l.sup.(m); .lamda..sub.l and .mu..sub.l
are the combining weights. K is the number of elements in the set
.OMEGA. i.e., the number of guard tones within an OFDM symbol. If
there are sixteen guard tones, by way of example, K is 16.
.lamda..sub.l and .mu..sub.l are chosen in the system design phase
so that in the absence of ACI, the following relationship
exists:
.sigma..times..times..times..lamda..times..times..mu..times.
##EQU00019## where E[X] denotes expectation or mean of a random
variable X. In the absence of ACI, this condition makes the mean of
.sigma..sub.aci.sup.(m)2(n) the same as the effective noise
variance. In the presence of ACI, this .sigma..sub.aci.sup.(m)2(n)
may be used as an estimate of the effective noise variance for the
"edge tones" (i.e., k=((N/2)-1) and k=-(N/2)). Note that the edge
tone at k=((N/2)-1) is the rightmost tone in the positive
frequency, and the edge tone at k=-(N/2) is the leftmost tone in
the negative frequency.
In the absence of ACI, the effective noise variance of the
band-edge should be the same as the in-band effective noise
variance. But in the presence of ACI, the band-edge effective noise
variance will be larger than the in-band effective noise variance.
Since the noise variance estimates are noisy, it may be possible
that .sigma..sub.aci.sup.(m)2(n)<{circumflex over
(.sigma.)}.sub.eff.sup.(m)2(n), which is not correct. Thus, the
term .sigma..sub.aci.sup.(m)2(n) can be refined as follows. The
maximum of .sigma..sub.aci.sup.(m)2(n) and the estimate for the
in-band tones are taken to be the variances for the edge tones:
.sigma..times..function..sigma..times..function..times..sigma..times..fun-
ction..sigma..times..function. ##EQU00020## where {circumflex over
(.sigma.)}.sub.eff.sup.(m)2(n) is the estimate of the in-band
effective noise variance for the n.sup.th OFDM symbol.
Next, the effective noise variance for the other band-edge tones,
{circumflex over (.sigma.)}.sub.eff,k.sup.(m)2(n) are interpolated
between in-band variance {circumflex over
(.sigma.)}.sub.eff.sup.(m)2(n) and {circumflex over
(.sigma.)}.sub.eff,N/2.sup.(m)2(n).
In the absence of ACI, the mean of
|Y.sub.k,l.sup.(m)-H.sub.k,l.sup.(m)|.sup.2 is
.times..times..times..times..times..times..sigma..times.
##EQU00021## Thus, the mean of g.sub.l.sup.(m) is
.times..times..times..times..times..times..sigma..times.
##EQU00022## since there are (G-1) elements in the sum. The mean of
|X.sub.k,l.sup.(m)|.sup.2 is .sigma..sup.(m)2, since there is no
signal in the guard tones. Accordingly, the mean of q.sub.l.sup.(m)
is given by the following equation:
.times..times..di-elect
cons..OMEGA..times..times..times..sigma..times..times. ##EQU00023##
where K is the number of guard tones. Thus, by properly choosing
.lamda..sub.l and .mu..sub.l, one can make the mean of
.times..lamda..times..times..mu..times. ##EQU00024## the same as
.sigma..sup.(m)2.
In the presence of ACI, g.sub.l.sup.(m) and q.sub.l.sup.(m) will
contain the ACI contributions. So the .sigma..sub.aci.sup.(m)2(n)
becomes larger than .sigma..sup.(m)2 to account for the increased
effective noise variance. This is used in LLR computation to
de-emphasize the LLRs from the band-edge tones.
Another example may be illustrative.
.lamda..sub.0=.lamda..sub.3=0,
.lamda..times..times..times..times..times..times..times..times..times..ti-
mes..times..times..mu..mu..mu..times..times..times. ##EQU00025##
where K is the number of guard-band tones within an OFDM symbol,
i.e. the number of elements in the set .OMEGA. and G-1 is the
number of band-edge pilot tones.
If only guard tones are used:
.lamda..lamda..lamda..lamda..times..times..mu..mu..mu..mu..times.
##EQU00026##
FIG. 8 is a flow diagram illustrating a method of estimating an
effective noise variance for the band-edge tones according to one
example. An average effective noise variance is estimated for the
band-edge tones from the band-edge pilot tones, the channel
estimates for the band-edge pilot tones, and the guard tones 802.
The edge tones of the OFDM symbol are assigned to an effective
noise variance equal to the maximum of the average effective noise
variance for the band-edge tones and the effective noise variance
for the in-band tones 804. The effective noise variance for the
band-edge tones are interpolated between the effective noise
variance of the edge tones and the effective noise variance of the
iii-band tones 806.
In the various embodiments of the receiver, methods for computing
the effective noise variances of OFDM symbols are described for
multiple antenna applications using diversity techniques. However,
the method described throughout this disclosure for computing noise
variances of OFDM symbols may have many applications. By way of
example, the noise variances of OFDM symbols may be useful for SNR
estimations. LLR computations, and other processing functions. In
multiple antenna applications. noise variance computations may be
used to determine which antenna is more reliable. It can also be
used to dc-emphasize the less reliable data and emphasize the more
reliable data received in OFDM symbols when computing LLRs. Those
skilled in the alt will readily appreciate that there may be
numerous applications in which noise variance information may be
useful.
The various illustrative logical blocks, modules, circuits,
elements, and/or components described in connection with the
embodiments disclosed herein may be implemented or performed with a
general purpose processor, a Digital Signal Processor (DSP), an
Application Specific Integrated Circuit (ASIC), a Field
Programmable Gate Array (FPGA) or other programmable logic
component, discrete gate or transistor logic, discrete hardware
components, or any combination thereof designed to perform the
functions described herein. A general-purpose processor may be a
microprocessor, but in the alternative, the processor may be any
conventional processor, controller, microcontroller, or state
machine. A processor may also be implemented as a combination of
computing components, e.g., a combination of a DSP and a
microprocessor, a plurality of microprocessors, one or more
microprocessors in conjunction with a DSP core, or any other such
configuration.
The methods or algorithms described in connection with the
embodiments disclosed herein may be embodied directly in hardware,
in a software module executed by a processor, or in a combination
of the two. A software module may reside in RAM memory, flash
memory, Read only Memory (ROM), Electrically Programmable ROM
(EPROM) memory, Electrically Erasable Programmable ROM (EEPROM)
memory, registers, hard disk, a removable disk, a Compact Disc ROM
(CD-ROM) or any other form of storage medium known in the art. A
storage medium may be coupled to the processor such that the
processor can read information from, and write information to, the
storage medium. In the alternative, the storage medium may be
integral to the processor.
The previous description of the disclosed embodiments is provided
to enable any person skilled in the art to make or use the present
invention. Various modifications to these embodiments will be
readily apparent to those skilled in the art, and the generic
principles defined herein may be applied to other embodiments
without departing from the spirit or scope of the invention. Thus,
the present invention is not intended to be limited to the
embodiments shown herein but is to be accorded the widest scope
consistent with the principles and novel features disclosed
herein.
* * * * *